The dual Lovász extension operator and the Shapley extension operator for TU games

An extension operator assigns to any TU game its extension, a mapping that assigns a worth to any non-negative resource vector for the players. Algaba et al. (2004) advocate the Lovász extension (Lovász, 1983) as a natural extension operator. This operator is determined by the minimum operator representing one particular CES (constant elasticity of substitution) technology. We explore alternative extension operators, the dual Lovász extension and the Shapley extension, that are based on the only two alternative CES technologies that induce an economically sound behavior of extensions in some sense, the maximum operator and the average operator.